It really didn't replace anything, I normally carry a J frame S&W. I wanted something pretty small with a larger capacity magazine. My eyes aren't great anymore and the X Ray night sights on the Sig are pretty good.
I shoot the P365 well, it has a pretty good trigger for a striker fired pistol, as accurate as any small pistol I've shot recently.
I've owned quite a few compact pistols over the last 40 years, every last one was either too thick and/or the trigger reach was at/above my limit (excepting the Kahr 9's). I was looking at the Glock 43, but have never shot the Glocks very well. The Glock is a great choice if you like the platform.
There have been a few issues with the early Sig's but the latest ones seem to be fine. Sig made a few improvements along the way, so we'll have to see how it performs long term.